Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions

2008 ◽  
Vol 78 (6) ◽  
Author(s):  
Goran Gligorić ◽  
Aleksandra Maluckov ◽  
Ljupčo Hadžievski ◽  
Boris A. Malomed
Keyword(s):  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bright Solitons ◽  
Dipole Interactions ◽  
The One

scholarly journals Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation

2014 ◽  
Vol 64 (1) ◽  
pp. 19-70 ◽  
Author(s):  
Fabrice Béthuel ◽  
Philippe Gravejat ◽  
Didier Smets
Keyword(s):  
Energy Space ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
The One

scholarly journals Study of Attractive Nonlinearity by 1-D Nonlinear Schrödinger Equation in the Bose–Einstein Condensate

1970 ◽  
Vol 33 (1) ◽  
pp. 87-98
Author(s):  
ML Rahman ◽  
Y Haque ◽  
SK Das ◽  
MM Hossain ◽  
MH Rashid
Keyword(s):  
Boundary Condition ◽  
Small Perturbation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
One Dimensional ◽  
Bright Solitons ◽  
Non Linear ◽  
The One ◽  
Bose Einstein ◽  
Academy Of Sciences

The work represents and investigates the stationary solutions of the one-dimensional Non-linear Schrödinger Equation (NLSE), for attractive non-linearity, in the Bose-Einstein condensates (BEC) under the box boundary condition and calculates the characteristics of internal modes of bright solitons (eigen modes of small perturbation of the condensate). DOI: 10.3329/jbas.v33i1.2953 Journal of Bangladesh Academy of Sciences, Vol. 33, No. 1, 87-98, 2009

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

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